Model reduction is a significant issue in dynamic system simulation and control, as a consequence of the unmanageable levels of storage and computational requirements for large-scale systems. In this paper, the concept of a balanced truncation approximation method is extended to large-scale systems with interval uncertainties to get the reduced-order model with uncertainties. In order to get the balanced system, the balancing transformation matrix is introduced by using the nominal system, and the reduced-order model with uncertainties is obtained by using balanced truncation. A major characteristic of this model reduction method is that the reduced-order model obtained in this way is also as uncertain as the original model. The closeness of the reduced-order model to the original model relies on the upper bounds of the ignored Hankel singular values. To compare the original model and the reduced-order model, a perturbation method is proposed to give the interval bounds of the responses of the original model and the reduced-order model. As applications of the proposed method, three numerical examples are given.
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